Why Does a Comet Have a Tail?

Image: NASA - Comet Pan-STARRS

Actually, comets have two tails. So, this is the tale of two tails. OK, that was a poor pun — I’m sorry. But comets are a hot item now. First, there is the comet Pan-STARRS as seen above. This isn’t the only comet of importance. Hopefully, in the fall of 2013 we will have a super awesome comet to look at — ISON. It might be the best comet since I don’t know when.

So let’s look at some interesting things about these comet tails. Be warned, I am not an astrophysicist. Instead, I am going to use some fundamental principles to try to explain why comets do what comets do. Oh, sure I could just look this stuff up. However, speculation is quite entertaining (at least for me).

What Is a Comet?

Image: NASA – Comet NEAT

Not every comet is the same, but it wouldn’t be terrible to say that a comet is a dirty-icy object in the solar system. When they come near the sun, they melt (I’m not sure “melt” is the most appropriate term here) and produce gas and dust. The gas and dust form both a coma and a tail (or two tails). If the comet is large enough and close enough to Earth, you can see the comet from the sunlight that reflects off this gas and dust.

Why Two Tails?

Image: NASA – Comet Hale-Bopp

There are two tails because there are two ways the comet can interact with the sun. Everyone thinks about light coming from the sun. However, there is also the solar wind. The solar wind is really just charged particles (like electrons and protons) that escape from the sun due to their high velocities. These charged particles then interact with the ionized gas produced from the comet.

The other tail is due to an interaction with the dust produced by the comet and the light from the sun. Really, it is this interaction that I want to talk about.

How Does Light Push on Matter?

Important idea number 1: Matter is made of positive and negative charges. If you have anything with structure (like dust particles) then it has to have atoms in it. Basically, dust is made of a combination of electrons, protons and neutrons. That’s it.

Important idea number 2: Light is an electromagnetic wave. What does this even mean? It can mean lots of things. For this discussion, the important thing is that if you have a region of space moving at the speed of light an electric and magnetic field can move in accordance with a set of rules we call Maxwell’s equations. Here is a typical representation of a sinusoidal EM wave from the awesome textbook Matter and Interactions.

Screen Capture from a Matter and Interactions Vpython program

The electric field and magnetic field in this light must both be perpendicular to each other and to the direction the wave moves. That’s important.

Important idea number 3: If you have a charged particle in an electric field, it will experience a force. For a positive charge, this force will be in the same direction as the electric field. For negative charges, the force is in the opposite direction as the electric field.

In the above diagram, I am using the yellow arrows to represent a region with a constant electric field. The red ball is a positive charge and the blue is a negative charge. The red and blue arrows represent the forces on these charges.

Important idea number 4: A moving electric charge will experience a force when moving in a magnetic field. The force will be perpendicular to both the magnetic field and the direction the charge is moving.

Just to make things a little bit more confusing, I am now using the yellow arrows to represent a magnetic field. In this diagram, the positive and negative charges are moving in opposite directions but both have a magnetic force in the same direction. Yes, I used red arrows to represent both the velocity of the charge and the magnetic force. Maybe that was a bad idea.

That’s all the important ideas. Now back to light. Suppose there is a positive charge sitting all by itself in empty space – not bothering anybody. Along comes some light – an electromagnetic wave. Here is an electromagnetic wave moving towards the charge.

When the EM wave first gets to the charge, there is no interaction with the magnetic field since the charge isn’t moving. However, the electric field interacts with the charge, it will exert a force and change it’s momentum. Once the charge is moving (say up in the diagram), there will be a magnetic force on that charge that pushes it in the same direction as the propagation of the EM wave.

What if it’s a negative charge? In that case, the electric field would make the negative charge move down in the diagram above. However, the magnetic force would still be in the same direction.

But isn’t the charge moving quite slowly? Yes – and that means the magnetic force is tiny. Light interacting with matter does not have a strong effect.

Ok, you know I cheated here, right? Of course this simplifies the interaction with light and matter quite a bit. However, I can at least show some possible way that light can push on matter. The pressure that light pushes on stuff can be written as:

Could you use this radiation pressure for some type of solar sail? If so, what would you call it? The answer is yes. It would be called a solar sail.

Image: NASA – artist’s concept of a solar sail

The basic idea is to create a large surface area so that even a small pressure could produce a significant force. Even a force of 1 or 2 Newtons would be good enough since it wouldn’t require any fuel and it would always be pushing. Of course the problem is making these sails that are big but don’t add much mass to the spacecraft. Oh – and there is the problem of getting into space. A solar sail would only be useful after the spacecraft is off the planet’s surface.

If Light Pushes on Dust, Wouldn’t It Push On the Comet?

The short answer is that light DOES push on the comet. Let’s look at two different pieces of dust in orbit near Mercury.

Let me call the radiation pressure at this point P. If the big dust has a radius twice that of the small dust, then I can calculate the force from the light on these two particles.

So, the bigger dust has a greater force. Just as expected. However, force doesn’t tell you everything. What about the acceleration? Let’s assume that both dust particles have the same density (ρ). Since there is just one force, the acceleration would be the force divided by mass. Oh, remember that the volume of a sphere is proportional to the radius cubed.

edit: I had left out the density. Added it in – h/t to Guillermo

So, the dust that is twice as big has half the acceleration. Although the force on the bigger dust is bigger, so is the mass. In fact if you double the radius of the dust, you triple the mass but only double the force from the light. Smaller dust has a greater acceleration. And this is why the dust gets pushed away from the comet, but the comet doesn’t get pushed to have the same trajectory.

Why Do the Two Tails Point in Different Directions?

I am going to have to make a simulation showing this dust trail – and trust me, I shall. The force on the dust is small. You can’t just look at the force from the light pressure, you have to still consider the gravitational force from the interaction with the sun. However, for the solar wind, this is a collision (well, an electrostatic interaction) between two masses. The charged particles from the sun are moving fast enough that this collision with the ionized gas results in the gas moving directly away from the sun. So, the interactions with the gas and dust result in different trajectories and tails pointing in different directions.